The maximum value of the applied force F such that the block as shown in the arrangement does not move is (Acceleration due to gravity, `g=10 ms^-2`)

Options

A. 20 N
B. 15 N
C. 25 N
D. 10 N

Explanation

Applied force on the block on a horizontal surface, as shown in the figure, we have

As we know that , force of friction `f=mu R`
From the diagram,
`f=mu(W+F sin60^@)`
`F cos60^@=1/(2sqrt3)(10sqrt3+F sin60^@)`
`impliesFtimes1/2=1/(2sqrt3)(10sqrt3+F timessqrt3/2){becausecos60^@=1/2sin60^@=sqrt3/2}`
`impliesF/2=1/(2sqrt3)timessqrt3(10+F/2)`
`implies F/2=1/2((20+F))/2impliesF=(20+F)/2`
`implies2F=20+Fimplies2F-F=20`
`therefore F=20N`